Biomedical Engineering Reference
In-Depth Information
selection system fails miserably. It turns out that there are often states that tend to
collect toomany events and states that collect too few. The other problem is that it does
not define what should happen when there are multiple highest weights. Which state
do you pick?
14.4.4.6 Stochastic Selection The answer to this dilemmawas to use a stochastic
process [12] to make the selection. Again, this sounds much more difficult than it
really is. An example helps make this clear. Suppose we only had five states and an
event generated the following five probability weights (0, 0.3, 0.4, 0.3, and 0).
Notice that the sum of these weights is unity. A stochastic selection process would
randomly choose the first state none of the time, the second state, 30% of the time,
the third state, 40% of the time, the fourth state, 30% of the time, and the last state,
0% of the time.
Usually, when we are analyzing data, we try to eliminate uncertainty. Cytome-
terists typically like nice, smooth data and contours, as they should. But in this case,
we let uncertainty guide our selection choice. As it turns out, stochastic selection was
the key that led to the ultimate success of this algorithm.
If we use this selection process to classify events into states and we let the system
find the optimal control definition point locations that minimize the nonuniformity of
the state frequencies, something quite unexpected happens.
14.4.4.7 Accounting for PopulationOverlap First, let me give some background.
For over 20 years, we have been perfecting cell cycle analysis methods that yield
accurate G1, S, and G2M estimates for complex DNA histograms. We have done
everything possible tomake these estimates as accurate as possible.We have hundreds
of generated histograms that we use to test our analysis procedures. Early in 2006, we
decided to test the probability state modeling system against our cell cycle analysis
product [13] to see how the S-phase estimates compared (see Figure 14.6). We were
astounded to discover that its accuracy was very comparable to the cell cycle
modeling package. This figure shows the correlation plot of S-phase estimates
from 150 synthesized DNA histograms. You can see an almost perfect correlation
between the two methods, indicating that the probability state modeling system
compensates for population overlap, at least as well as a DNA modeling package.
How is this possible? If you look carefully at the analyses of a single DNA listmode
file (Figure 14.7), you can begin to appreciate why the probability state model
accounts for most of the population overlap between G1 and S, and S and G2M. Since
the probability state model represents parameter values and their uncertainty on the y-
axis (see vertical arrows) and we find our percentages on the x-axis (see horizontal
arrows), we are automatically accounting for overlap due to measurement error. You
will need to examine this figure for a while to convince yourself of this fact. There is
uncertainty in the control definition point
s position along the x-axis, but most of that
uncertainty is due to counting error, not measurement error.
What is exciting about this attribute of probability state models is that the
subregions or zones along the probability state axis can be defined by any number
of correlated parameters. Thus, this method solves the population overlap problem in
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